1. AREAS OF COMMON POLYGONS
Unit 26
AREAS OF COMMON POLYGONS

2. AREAS OF RECTANGLES
A rectangle is a four-sided polygon with opposite sides equal and parallel and with each angle equal to a right angle
The area of a rectangle is equal to the length times the width
Determine the area of the figure shown below:
7 in
3.5 in
Area = length  width
= 7 in  3.5 in
= square inches Ans

3. AREAS OF PARALLELOGRAMS
A parallelogram is a four-sided polygon with opposite sides parallel and equal
The area of a parallelogram is equal to the product of the base and height
Area = base × height

4. AREAS OF PARALLELOGRAMS
Find the base of a parallelogram given that its area is 164 square meters and its height is 16 meters:
Area = base  height
Substitute in the given measurements and transpose the formula for the base
164 m2 = b  16 m
b = m Ans

5. AREAS OF TRAPEZOIDS
A trapezoid is a four-sided polygon that has only two sides parallel
Common trapezoids
Ramps (loading and jumping)
Utility knife blades
Door stops (some not all)
The area of a trapezoid is equal to one half the product of the height and the sum of the bases
Area = ½(b1 + b2)h

6. AREAS OF TRAPEZOIDS (Cont)
Find the cross sectional area of the hot tub shown below
4.75ft
8.5 ft
10.25 ft
Area = ½ (b1 + b2) h
= ft2 Ans

7. AREAS OF TRIANGLES
The area of a triangle is equal to one-half the product of the base and height
Determine the area of the gable end of your home:
- Notice the isosceles triangle, so use Pythagorean Theorem to get your height.
Area = 1/2 the base times the height
15.5 m
= 1/2 (26.75 m)(15.5 m)
= m2 Ans
26.75 m

8. AREAS OF TRIANGLES GIVEN THREE SIDES
When three sides of a triangle are known and the height is unknown, Hero’s (Heron’s) Formula can be used to determine its area
Where: A = area; a, b, and c = sides; and s = 1/2 (a + b + c)

9. AREAS OF TRIANGLES GIVEN THREE SIDES
Find the area of a triangle with sides of 10m,16m, and 20m:
Where: A = area; a, b, and c = sides; and s = 1/2 (a + b + c)
First find s:
s = 1/2 (a + b + c) = 1/2 (10 m + 16 m + 20 m) = 23 m

10. PRACTICE PROBLEMS
A rectangular piece of wood is 4 feet wide and 6.5 feet long. Find the area of the wood in square feet.
How much would the piece of wood in problem #1 cost if it sells for $0.12 per square foot?
Determine the height of a parallelogram given that it has an area of square inches and a base of 16.2 inches.

11. PRACTICE PROBLEMS (Cont)
The cross section of a wooden planter is in the shape of a trapezoid with a height of cm and bases of 34.2 cm and 18.4 cm. Find the cross-sectional area of the planter in square centimeters.
Find the missing base of a trapezoid given that it has an area of 154 in2, a height of 8.8 in, and the known base is 14.2 inches.
Determine the height of a triangle given that it has an area of 100 square meters and a base of 6.25 meters.

12. PRACTICE PROBLEMS (Cont)
Find the area of a triangle with sides of 12 mm, 15 mm, and 18 mm.
Determine the area of the end of a parking block pictured below:
5 in
8 in
14 in
7 in

13. PROBLEM ANSWER KEY 26 ft2 $3.12 9.5 inches 12805.47 cm2 20.8 inches
32 meters
mm2
164.5 in2